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Say 20 cards are dealt from a 52 card deck. What is the probability that there are more spades than face cards?

User Dejavu
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Final answer:

This high school-level mathematics question asks about the probability of drawing more spades than face cards out of 20 dealt cards from a shuffled deck.

Step-by-step explanation:

The question concerns the probability of drawing more spades than face cards from a shuffled deck when 20 cards are dealt. Since we know there are 13 spades in a deck, and 12 face cards (which include Jack, Queen, and King from each of the four suits), we must calculate the various combinations in which the number of spades drawn exceeds the number of face cards drawn out of the 20 cards. This involves complex combinatorial calculations because you need to account for the various ways this event can occur. Also, this question implies knowledge of advanced probabilities and combinations which go beyond the usual high school curriculum and might require computational assistance for exact probabilities.

We're comparing the quantity of spades to the combined count of all face cards irrespective of their suit. To calculate this probability, one would generally use combinatorial formulas or computational methods to sum the probabilities of all possible outcomes where the number of spades exceeds the number of face cards in the 20-card draw.

User Bitwelder
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